8 research outputs found
Accurate Adiabatic Connection Curve Beyond the Physical Interaction Strength
The adiabatic connection curve of density functional theory (DFT) is
accurately calculated beyond the physical interaction strength for Hooke's
atom, two interacting electrons in a harmonic well potential. Extrapolation of
the accurate curve to the infinite coupling limit agrees well with the strictly
correlated electron (SCE) hypothesis but the approach to this limit is more
complex. The interaction strength interpolation is shown to be a good, but not
perfect, fit to the adiabatic curve. Arguments about the locality of
functionals and convexity of the adiabatic connection curve are examined in
this regime.Comment: 7 pages, 5 figure
Homotopy probability theory II
This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework can assist in the development of homotopy probability theory, where a vector space of random variables is replaced by a chain complex of random variables. This allows the principles of derived mathematics to participate in classical and noncommutative probability theory. A simple example is presented.1111sciescopu